Decay properties of spectral projectors with applications to electronic structure

Motivated by applications in quantum chemistry and solid state physics, we general results from approximation theory and matrix analysis to the of the decay properties of spectral projectors associated with large and Hermitian matrices. Our theory leads to a rigorous proof of the off-diagonal decay ("nearsightedness") for the density matrix of systems at zero electronic temperature in both orthogonal and-orthogonal representations, thus providing a firm theoretical basis for the of linear scaling methods in electronic structure calculations for-metallic systems. We further discuss the case of density matrices for systems at positive electronic temperature. A few other possible are also discussed.